Page 397 - Elements of Chemical Reaction Engineering Ebook

i
368 ' Nonelementary Reaction Kinetics Chap. 7

7.3.3 Modeling a Batch Polymerization Reactor
To conclude this section we determine the concentration of monomer as
a function of time in a batch reactor. A balance on the monomer combined
with the LCA gives

Monomer - dM -- - k,M Rj = k,MRL = kPM (7-39)
balance dt
A balance on the initiator Z2 gives

dZ
Initiator i. -
=
balance 2 k0Z2
dt
t. Integrating and using the initial condition Z2 = Zz0 at t = 0, we obtain the equa-
. .
. tion pf the initiator concentration profile:
I2 = Z20 exp(-kot) (7-40)
1 Substituting for the initiator concentration in Equation (7-39), we get
- 2k0 120 f 1 /2 (7-41)
dM = -kpM[~) exp[--:t)
dt

Integration of Equation (7-41) gives

(7-42)

One'motes that as t __j m, there will still be some monomer left unre-
acted. Why?
A plot of monomer concentration is shown as a function of time in Fig-
ure' 7-5 for "different initiator concentrations.
The fractional conversion of a monofunctional monomer is

x=- Mo-M
M0
We see from Figure 7-5 that for an initiator concentration 0.001 M, the mono-
mer concentration starts at 3 M and levels off at a concentration of 0.6 M, cor-
responding to a maximum conversion of 80%.
Now that we can determine the monomer concentration as a function of
time, we will focus on determining the distribution of dead polymer, P,. The
concentrations of dead polymer and the molecular weight distribution can be
derived in the following manner. lo The probability of propagation is

.b
''E. J. Schork, P. B. Deshpande, K. W. Leffew, Control of Polymerization Reactor. New
York: Marcel Dekker (I 993).